Related papers: Exact Analytical Parallel Vectors
We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs to the boundary between half-planes. These parameters…
We classify maximal quartic generalised projective special real curves up to equivalence. A maximal quartic generalised projective special real curve consists of connected components of the intersection of the hyperbolic points of a quartic…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
A graph embedding algorithm embeds a graph into a low-dimensional space such that the embedding preserves the inherent properties of the graph. While graph embedding is fundamentally related to graph visualization, prior work did not…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
Laplacian eigenvectors capture natural community structures on graphs and are widely used in spectral clustering and manifold learning. The use of Laplacian eigenvectors as embeddings for the purpose of multiscale graph comparison has…
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via…
In mathematics curves are typically defined as the images of continuous real functions (parametrizations) defined on a closed interval. They can also be defined as connected one-dimensional compact subsets of points. For simple curves of…
We study parameter spaces of linear series on projective curves in the presence of unibranch singularities, i.e. {\it cusps}; and to do so, we stratify cusps according to value semigroup. We show that {\it generalized Severi varieties} of…
Many finite dimensional integrable systems qre expressed with the help of the Lax equation which highlights a spectral parameter and therefore a spectral curve. These spectral curves are the starting point of an algebro-geometric…
Absolute parallelism geometry is frequently used for physical applications. It has two main defects, from the point of view of applications. The first is the identical vanishing of its curvature tensor. The second is that its autoparallel…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The…
In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields.
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…